Thermally-activated magnetization dynamics of small nanoparticles subject to microwave (AC) external fields is studied. It is shown that, under sufficiently strong microwave excitations, chaotic magnetization dynamics may occur close to saddle-type heteroclinic connections, and this heteroclinic chaos is responsible for the erosion of the safe basin around stable magnetization states. The erosion phenomenon is then connected to the escape problem from the energy well surrounding a stable equilibrium. It is shown that escape times follow a generalized Arrhenius law governed by temperature, microwave field amplitude, frequency and heteroclinic chaos threshold.